Lc helices and harmonic curvatures in space forms (hypersurface)

Abstract

In n-dimensional Euclidean space E^n, harmonic curvatures of a non-degenerate curve defined by \"Ozdamar and Hacisaliho\u{g}lu [4]. In this paper, We define a new type of curves called LC helix when the angle between tangent of this curve and LC parallel vector field in space form is constant. Furthermore, several characterizations of these curves by using its harmonic curvatures are obtained. Particularly, in the 3-dimensional spaceform we obtain the results [5].